1 4) Linearize the nonlinear dynamic system given below at one of its equilibria. 1 (2 + cos(x))* + xx + sin(x) x + cosx = 0 Rewrite the equation using the state vector of q = [91921" = [xx]"as 92 -69192 + sin(91) a + cos 9)/(2 + cos(91) --[-gacz + sinadai 1 = f(9) (1) At the equilibrium, we have f(q)q=q* = [0 0]", find the equilibria and pick one. The Taylor series expansion rafi afi f(q) + 091 092 |afa afz .(9-9") WAS f(q) Laq 092-q=0 With 8 = 9 -q linearized coordinate vector. Thus the linearized model about q* becomes S = A8 (2) Simulate the nonlinear (1) and linear (2) systems in Simulink with the initial condition is set close to the equilibrium selected. Say you pick q* = [)"then you may select the initial condition 4. = [1.2 0j